Graphene mounted on aerogel

ABSTRACT

An apparatus having reduced phononic coupling between a graphene monolayer and a substrate is provided. The apparatus includes an aerogel substrate and a monolayer of graphene coupled to the aerogel substrate.

BACKGROUND

The present application relates generally to the field of mechanicalsupports for graphene sheets. The present application relates morespecifically to the field of graphene sheets mounted on aerogelsubstrates.

Phononic coupling between graphene and a supporting substrate canmarkedly reduce its in-plane electron mobility. For example,freestanding graphene has a mu value of approximately 200,000 cm²/V-sec.However, direct mounting on a silicon substrate can reduce this value toapproximately 1000 cm² /V-sec. Thus, there exists a need for an improvedmechanical support for a graphene film.

SUMMARY

One embodiment relates to an apparatus having reduced phononic couplingbetween a graphene monolayer and a substrate. The apparatus includes anaerogel substrate and a first monolayer of graphene coupled to theaerogel substrate.

Another embodiment relates to a system having preserved electronicproperties in a supported graphene sheet. The system includes a graphenesheet supported by an aerogel substrate, the graphene sheet includingone or more devices.

Another embodiment relates to a method of reducing phononic couplingbetween a graphene monolayer and a substrate. The method includesproviding a substrate formed of aerogel and placing a monolayer film ofgraphene in contact with the substrate.

Another embodiment relates to a method of preserving electronicproperties in a mechanically supported graphene sheet. The methodincludes providing a substrate formed of aerogel, providing a graphenefilm having one or more devices disposed thereon, and disposing thegraphene film on the substrate.

Another embodiment relates to a method of forming a circuit board. Themethod includes providing a graphene film having one or more devicesdisposed thereon, providing a substrate formed of aerogel, the substratehaving a first side and a second side opposite the first side, disposinga first portion of the graphene film on the first side of the substrate,and disposing a second portion of the graphene film on the second sideof the substrate.

Another embodiment relates to a circuit board. The circuit boardincludes a first substrate formed of aerogel, the first substratecomprising a first side and a second side opposite the first side, and agraphene film having a first portion and a second portion and having oneor more devices disposed thereon. The first portion of the graphene filmis disposed adjacent the first side of the substrate, and the secondportion of the graphene film is disposed adjacent the second side of thesubstrate.

The foregoing is a summary and thus by necessity containssimplifications, generalizations and omissions of detail. Consequently,those skilled in the art will appreciate that the summary isillustrative only and is not intended to be in any way limiting. Otheraspects, inventive features, and advantages of the devices and/orprocesses described herein, as defined solely by the claims, will becomeapparent in the detailed description set forth herein and taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic plan view of a portion of a graphene sheet, shownaccording to an exemplary embodiment.

FIG. 2 is a schematic plan view of a portion of a graphene sheet, shownaccording to another embodiment.

FIG. 3 is a schematic elevational view of a graphene sheet and asubstrate, shown according to an exemplary embodiment.

FIGS. 4A-4E are schematic elevational views of aerogel substrates andgraphene sheets, shown according to various embodiments.

FIG. 5A is a schematic cross-sectional elevational view of a substrateand a graphene sheet, shown according to an exemplary embodiment.

FIG. 5B is a schematic plan view of a substrate and a graphene sheet,shown according to an exemplary embodiment.

FIGS. 6A-6C are schematic elevational views of aerogel substrates andgraphene, shown according to various embodiments.

FIG. 7A is a schematic elevational view of a substrate and a graphenesheet, shown according to another embodiment.

FIG. 7B is a schematic plan view of a substrate and a graphene sheet,shown according to another embodiment.

FIGS. 8A-8B are schematic cross-sectional elevational views of asubstrate and a graphene sheet, shown according to various embodiments.

FIGS. 9A-9B are schematic elevational views of a substrate and agraphene sheet, shown according to various embodiments.

FIGS. 9C is a schematic perspective views of interwoven substrates andgraphene sheets, shown according another embodiment.

FIG. 10 is a flowchart of a process for reducing phononic couplingbetween a graphene monolayer and a substrate, shown according to anexemplary embodiment.

FIG. 11 is a flowchart of a process for reducing phononic couplingbetween a graphene monolayer and a substrate, shown according to anotherembodiment.

FIG. 12 is a flowchart of a process for reducing phononic couplingbetween a graphene monolayer and a substrate, shown according to anotherembodiment.

FIG. 13 is a flowchart of a process for reducing phononic couplingbetween a graphene monolayer and a substrate, shown according to anotherembodiment.

FIG. 14 is a flowchart of a process for reducing phononic couplingbetween a graphene monolayer and a substrate, shown according to anotherembodiment.

FIG. 15 is a flowchart of a process for reducing phononic couplingbetween a graphene monolayer and a substrate, shown according to anotherembodiment.

FIG. 16 is a flowchart of a process for preserving electronic propertiesin a mechanically supported graphene sheet, shown according to anexemplary embodiment.

FIG. 17 is a flowchart of a process for preserving electronic propertiesin a mechanically supported graphene sheet, shown according to anotherembodiment.

FIG. 18 is a flowchart of a process for preserving electronic propertiesin a mechanically supported graphene sheet, shown according to anotherembodiment.

FIG. 19 is a process for forming a circuit board, shown according to anexemplary embodiment.

DETAILED DESCRIPTION

Referring generally to the figures, systems and methods using graphenemounted on aerogel and components thereof are shown according toexemplary embodiments. Graphene is a one-atom-thick layer of carbonatoms packed in a honeycomb lattice. Graphene has several advantageouselectronic properties including high electron mobility, high thermalconductivity, small nuclear magnetic moments, and high permittivity.Graphene further has an advantageous density state, advantageouselectronic, optical, and plasmonic band structures, and otheradvantageous electronic, optical, and quantum-mechanical properties.These properties are particularly present in monolayer (one-atom-thick)sheets or films of graphene, which substantially behave as a singlecrystalline material. Sheets of substantially randomly arranged graphenenanostructures have discontinuities and portions arranged in non-planarfashions, and thus behave like polycrystalline or amorphous materials,causing scattering of phonons and diminishing the beneficial propertiesof the graphene sheet.

Supporting a graphene sheet on a conventional substrate, such as asilicon substrate, diminishes the beneficial properties of graphenebecause the graphene sheet phononically couples to the substrate. Theconventional method of combating the phononic coupling is to suspend thegraphene in free space over a trench in the substrate. However, thismethod results in the graphene being inherently unsupported. Moreover,the trenched and non-trenched regions create non-uniform properties inthe graphene and limit the applications of graphene. For example, it maybe preferred to mechanically support a macroscopic sheet of graphene.

One way to limit the loss of mobility and other advantageous propertiesof graphene is to mount the graphene sheet on a porous substrate ratherthan a full density one. One porous material that may be used is aerogel(e.g., aerojelly, frozen smoke, solid air, etc.). Aerogel is formed froma gel in which the liquid component has been replaced with a gas. Thesol-gel process or super-critical drying may be used to make aerogel.The aerogel may be made from silica, carbon, carbon oxides, alumina,chromia, etc. Carbon aerogels can include carbon nanotube or grapheneaerogels.

Using aerogel as a substrate for the graphene sheet provides amechanical support for the graphene sheet while decreasing the couplingconstant between the graphene sheet and the substrate. Decreasing thecoupling constant reduces phononic coupling effects and minimizessubstrate-induced effects on the electronic, optical, andquantum-mechanical properties of the graphene film.

Before discussing further details of the graphene-aerogel systems andmethods and the components and uses thereof, it should be noted that forpurposes of this disclosure, the term coupled means the joining of twomembers directly or indirectly to one another. Such joining may bestationary in nature or moveable in nature and such joining may allowfor the flow of fluids, electricity, electrical signals, or other typesof signals or communication between the two members. Such joining may beachieved with the two members or the two members and any additionalintermediate members being integrally formed as a single unitary bodywith one another or with the two members or the two members and anyadditional intermediate members being attached to one another. Suchjoining may be permanent in nature or alternatively may be removable orreleasable in nature.

Referring to FIGS. 1-2, schematic plan views of a portion of a graphenesheet 10 are shown according to exemplary embodiments. Graphene forms ahexagonal or honeycomb lattice of carbon atoms 12. A monolayer graphenesheet or film comprises a substantially two-dimensional, one-atom-thickplane. For the purposes of this application, the carbon lattice of thegraphene sheet is referred to as being a plane even though in practice,the sheet may have waves or ripples passing therethrough, or may exhibitcurvature on a macro scale. One of skill in the art will understand thatthe graphene sheet has planar properties even though it may not meet astrict geometric definition of a plane.

Graphene sheets may be formed in a variety of ways including, but notlimited to, drawing, epitaxial growth, vapor deposition, etc. Thegraphene sheet may be pure (e.g., an all-carbon honeycomb lattice) ordoped. Doping may occur in a variety of ways. Referring to FIG. 2, agraphene sheet may be doped with non-carbon atoms. For example, nitrogenatoms 14, boron atoms 16, phosphorus atoms, and/or sulfur atoms may beinserted or formed into the carbon lattice. As shown, doping may createone or more holes 18 or other defects in the lattice. Another method ofdoping the graphene sheet (not shown) is to modify (e.g., cut, etc.) alateral edge of the graphene sheet to create a non-uniform (e.g.,ragged, substantially non-linear, etc.) boundary shape.

Referring to FIG. 3, a schematic elevation view of the graphene sheet 10and a substrate 30 is shown, according to an exemplary embodiment. Thegraphene sheet 10 may be doped with one or more functional groups 20that extend out of the graphene plane 22. The functional group may beselected from any suitable functional group, including, but not limitedto, oxygen (i.e., graphene oxide), hydrogen (e.g., graphane), fluorine,methyl, ethyl, ester, phenol, hydrocarbyl, haloalkane, polypeptides,etc. The hydrogen or graphane functional groups cause the graphene sheet10 to act as an insulator. The graphene sheet 10 may be functionalizedat one or more sites. According to one embodiment, the graphene sheet 10may be functionalized at all sites. The graphene sheet 10 may befunctionalized only on the side adjacent the substrate 30, only on theside opposite the substrate 30, or any combination thereof. As shown,the graphene sheet 10 may bond to the substrate 30 via one or morefunctional groups 20.

Referring to FIGS. 4A-4D, schematic elevation views of aerogelsubstrates 30 and graphene sheets 10 are shown, according to exemplaryembodiments. FIG. 4A shows an aerogel substrate 30 having asubstantially homogeneous surface 32, which supports the graphene sheet10. The substrate 30 is further shown to have uniform properties indepth. As shown, the graphene sheet 10 is in planar contact with thesurface 32 of the aerogel substrate 30. The graphene sheet 10 may coupleto the aerogel substrate 30 at some or all of the carbon sites.According to one embodiment, the graphene sheet 10 does not couple to atleast some of the sites. Reducing the number of coupling sites betweenthe graphene sheet 10 and the substrate 30 generally reduces thephononic coupling between the graphene sheet 10 and the aerogelsubstrate 30. At these uncoupled sites, the graphene sheet 10 mayripple. FIG. 4B shows the aerogel substrate 30 having a structuredsurface. One or more structures 34 may extend laterally and may becoordinated with graphene sites where minimal perturbation of in-planeproperties is important. For example, the structures 34 may beconfigured to support the graphene sheet 10 at nodes or antinodes.According to various embodiments, the structures 34 may be posts formedof aerogel or nanotubes. The nanotubes may be formed of carbon (e.g., ifa carbon based aerogel) or silicon (e.g., if a silica based aerogel).

According to the embodiment shown in FIG. 4C, the aerogel substrate 30may be two sided. A first side 36 is shown to have a structured surface34, and a second side 38 is shown to have a substantially homogenoussurface 32. FIG. 4D shows a two-sided aerogel substrate 30 having astructured surface 34 on each side. The first side 36 is shown toinclude a first structured surface 34 a, and the second side 38 is shownto include a second structure surface 34 b. Having different structureson each side of the substrate may result in different properties on eachside of the substrate 30.

According to the embodiment shown in FIG. 4E, the aerogel substrate 30properties may vary with depth. As shown, the substrate 30 includes asurface layer 40 near the graphene supporting surface (e.g., structuredsurface 34 homogeneous surface 32, as shown) and a bulk layer 42. Thetransition between the surface layer 40 and the bulk layer 42 may begradual or distinct, and the substrate 30 may include any number ofintermediary layers. According to one embodiment, the surface layer 40may be configured to have a different density than the bulk layer 42.According to another embodiment, referring generally to FIG. 3, thesurface layer 40 may be configured to chemically bond to functionalgroups 20 extending from the graphene sheet 10.

Referring to FIGS. 5A-5B, schematic diagrams of an aerogel substrate 30and a graphene sheet 10 are shown, according to an exemplary embodiment.The substrate 30 is shown to include lateral support structures 44disposed at a lateral edge of the graphene sheet 10. The lateral supportstructures 44 may be configured to laterally support the graphene sheet10. The structures 44 may be coordinated with graphene sites whereminimal perturbation of in-plane properties is important. For example,structures 44 may be configured to support the graphene sheet 10 atnodes or antinodes. For example, as shown in the enlarged top plan viewof FIG. 5B, the lateral support structures 44 may be coordinated withselected sites. The embodiment of FIGS. 5A and 5B shows the lateralsupport structures 44 to be formed of the aerogel substrate. Accordingto other embodiments, the lateral support structures may be anothercomponent and formed of another material. For example, the lateralsupport structures may extend from supports configured to restrain thesubstrate 30.

Referring to FIGS. 4A and 6A-6C, schematic block diagrams of aerogelsubstrates 30 and graphene sheets 10 are shown, according to exemplaryembodiments. As shown in FIG. 4A, the substrate 30 includes a first side36 configured to support the graphene sheet 10. According to anexemplary embodiment, the graphene sheet 10 is a monolayer film coupledto the aerogel substrate 30. According to the embodiment shown in FIG.6A, a substrate 30 is disposed on each side of the graphene sheet 10. Asshown, a first substrate 30 a supports a first side 24 of the graphenesheet 10, and a second side 26 of the graphene sheet 10 supports asecond substrate 30 b. One or more additional graphene sheets 10 may bestacked on the free side of one of the substrates 30.

According to the embodiment shown in FIG. 6B, the substrate 30 includesa first side 36 configured to support a first graphene sheet 10 a and asecond side 38 opposite the first side 36 configured to support a secondgraphene sheet 10 b. One or both of the first and second graphene sheets10 a, 10 b may be a monolayer of graphene. According to one embodiment,the second side could be a lateral side 46 of the substrate 30.According to other embodiments a second substrate 30 may be stacked onthe free side of one of the graphene sheets 10 a, 10 b.

The graphene-substrate-graphene configuration of FIG. 6B may beconfigured as a capacitor, e.g., to form a static electric field betweenthe graphene sheets 10 and across the substrate 30. The first graphenesheet 10 a may be configured to receive a first electrical charge. Forexample, the first graphene sheet 10 a may be coupled to a firstelectrical contact 50 a. Similarly, the second graphene sheet 10 b maybe configured to receive a second electrical charge. For example, thesecond graphene sheet 10 b may be coupled to a second electrical contact50 b. A voltage may be applied across the first and second electricalcontacts 50 a, 50 b. Accordingly, positive or negative charges willbuild up on the first and second graphene sheets 10 a, 10 b depending onthe polarity of the voltage applied.

According to the embodiment shown in FIG. 6C, a first side 24 of thegraphene sheet 10 a is supported by the substrate 30. A second graphenesheet 10 b is disposed on the second side 26 of the first graphene sheet10 a. As shown, a first side of the second graphene sheet is disposedadjacent to the second side 26 of the first graphene sheet, opposite thesubstrate 30. A third graphene 10 c sheet may be disposed on or adjacenta second side of the second graphene sheet 10 b, opposite the firstgraphene sheet 10 a and the substrate 30. Another graphene sheet 10 oranother substrate 30 may be disposed on the free side of the thirdgraphene sheet 10 c. According to various embodiments, graphene sheetsmay be in intimate contact with each other, thereby acting as a bi-layeror tri-layer graphene sheet.

According to various embodiments, the layering of graphene sheets 10 andsubstrates 30 may be continued in a variety of combinations. Forexample, the substrate-graphene-substrate combination of FIG. 6A may bedisposed on the graphene-aerogel-graphene combination of FIG. 6B to formone stack. It should also be noted that a substrate 30 may be coupled toanother substrate 30. For example, substrates 30 having differentproperties may be coupled together to provide different properties onopposite sides of the combined substrate 30.

In any of the configurations described above, a graphene sheet 10 may bechemically bonded, unbonded, mechanically coupled, or any combinationthereof to a substrate 30 or to another graphene sheet 10. The type ofinteraction between layers (e.g., bonded, unbonded, or mechanicallycoupled) may be the same or different between different layers of thestack. For example, in FIG. 6B, the top graphene sheet 10 a may beunbonded to the substrate 30, whereas the bottom graphene sheet 10 b maybe bonded to the substrate. It is further contemplated that additionalgraphene sheets 10 may or may not be monolayers of graphene, and theadditional substrates 30 may or may not be formed of aerogel. Thegraphene sheets 10 and substrates 30 may be co-formed, or may be formedseparately and subsequently joined. According to one embodiment, a firstgraphene sheet is co-formed on a first aerogel substrate, and a secondgraphene sheet is co-formed on a second aerogel substrate. The firstaerogel substrate is then mounted on the second graphene sheet to form astack.

The properties of the graphene sheet 10 may change with tension orcompression. For example, the normal mode of the graphene sheet 10 maybe raised as one or more tensile forces are applied, which may causechanges to the electronic, optical, thermal, and quantum properties ofthe sheet 10. It is contemplated that tensile or compressive forces maybe applied to the graphene sheet 10 in one or more ways. According toone embodiment, the graphene sheet 10 may be heated prior to beingdisposed on the aerogel substrate 30. Accordingly, as the graphene sheet10 cools, the substrate 30 may hold the sheet 10 in tension. Accordingto another embodiment, the graphene sheet 10 may be formed at a firsttemperature and configured to operate at a second temperature (e.g.,operating temperature, upper limit of an operating temperature range,mean operating temperature, etc.) which is lower than the firsttemperature. The graphene sheet 10 may then be disposed on the substrate30 while above the second temperature. Accordingly, as the graphenesheet 10 cools, the substrate 30 may hold the sheet 10 in tension, andsome tension will be maintained up to the operating temperature of thegraphene sheet 10. According to another embodiment, the substrate 30 maybe chilled prior to the application of the graphene sheet 10.Accordingly, the substrate 30 will apply tension to the graphene sheet10 as the substrate 30 expands as it returns to a nominal temperature.According to another embodiment the aerogel substrate 30 may be heatedbefore the graphene sheet 10 is disposed thereon. Accordingly, as theaerogel substrate 30 cools, a compressive force is applied to thegraphene sheet 10. According to another embodiment, the graphene sheet10 may be cooled prior to be disposed on the aerogel substrate 30; theaerogel substrate 30 thus applying compressive forces to the graphenesheet 10 as the graphene sheet 10 warms to the temperature of theaerogel substrate 30. According to yet another embodiment, the graphenesheet 10 may be formed at a first temperature and configured to operateat a second temperature (e.g., operating temperature, upper limit of anoperating temperature range, mean operating temperature, etc.) which ishigher than the first temperature. The graphene sheet 10 may then bedisposed on the substrate 30 while below the second temperature.Accordingly, as the graphene sheet 10 warms, the substrate 30 compressthe sheet 10, and some compression will be maintained up to theoperating temperature of the graphene sheet 10.

Referring generally to FIGS. 7A-7B, the graphene sheet 10 may bemechanically stretched. According to one embodiment, the graphene sheet10 may be mechanically stretched prior to being mounted on the substrate30, and the substrate 30 then holding the graphene sheet 10 in tension.For example, the one or more support structures 34, or lateral supportstructures 44, may be configured to maintain tension on the graphenesheet 10. The graphene sheet 10 may be stretched in one or moredirections prior to mounting in order to achieve desired properties.

According to the embodiment schematically shown in FIGS. 7A-7B, one ormore tensioners 52 (e.g., mechanical coupling, clamp, structure, etc.)may be configured to provide a tensile force to the graphene sheet 10.FIG. 7A shows two opposed tensioners 52 a, 52 b which may be drawn inopposite directions, for example, by a servo-motor, variable magneticfield, magnetostriction, piezoelectric actuators, etc. FIG. 7B shows aplurality of tensioners 52 configured to apply tensile forces in morethan one direction. For example, first tensioners 52 a, 52 b areconfigured to pull the graphene sheet 10 in a first direction, andsecond tensioners 52 c, 52 d are configured to pull the graphene sheet10 in a second direction. Tensioners 52 may be configured to pull thegraphene sheet in any number of directions. For example, three pairs oftensioners may be oriented and configured to pull the graphene sheet 10in the directions of the graphene lattice.

According to one embodiment, the tensioners 52 may be configured suchthat they may provide a selectable tensile force to the graphene sheet10. Providing a selectable tensile force to the graphene sheet 10enables tuning of the graphene sheet 10 to achieve desired properties.For example, applying tensile forces in certain directions may makecertain properties of the graphene sheet 10 directionally dependent.

According to one embodiment, the graphene sheet 10 may be fixed at oneend, for example, coupled to the substrate 30 or other fixed structure,and pulled by an opposing tensioner 52. According to another embodiment,the graphene sheet 10 may be pre-stretched, as described above, andcoupled to the tensioners 52 in a stretched state. Accordingly, thetensioners 52 would maintain the tension on the graphene sheet 10.

Referring to FIGS. 8-9, the graphene sheet 10 may be configured tosupport one or more devices 56, shown as a first through third devices56 a, 56 b, and 56 c. According to various embodiments, the one or moredevices 56 may include a photonic circuit, a plasmonic circuit, anelectronic circuit, an integrated circuit, a microelectromechanicalsystem, a nanoelectro-mechanical system, etc., or a combination thereof.The devices 56 may be formed by doping, functionalizing, etching,cutting, shaping, or applying electrical fields to the graphene sheet10. The devices 56 may be configured to take advantage of the electronicproperties (e.g., electron mobility, electron transport, bandstructures, density of states, etc.) of the graphene sheet 10. Usingaerogel as a substrate 30 for the graphene sheet 10 mechanicallysupports the graphene sheet 10 while reducing phononic coupling betweenthe graphene and the substrate 30, thus reducing substrate-inducedeffects in the graphene and preserving the electron properties in thegraphene sheet 10. As described above, these device-including graphenesheets 10 maybe coupled or mounted to one or more sides of a substrate30.

As shown in FIGS. 8A-8B, a first graphene sheet 10 a including a firstdevice 56 a is disposed on a first side of the substrate 30, and asecond graphene sheet 10 b including a second device 56 b is disposed ona second side of the substrate 30. It is contemplated that graphenesheets 10 may be disposed one or more lateral sides 46 of the substrate30. The first and second sheets 10 a, 10 b of graphene may beoperatively coupled. According to various embodiments, the graphenesheets 10 may be electronically, phononically, plasmonically,photonically, and/or quantumly coupled. According to the embodimentshown in FIG. 8A, the substrate 30 includes an opening 54 (e.g.,through-hole, via, aperture, etc.) extending from the first side 36 ofthe substrate 30 to the second side 38 of the substrate. The first andsecond graphene sheets 10 a, 10 b may be coupled through the opening 54.For example, the opening 54 may be lined with a conductive material, ananotube may extend through the opening 54, or a connecting structuremay pass through the opening 54. According to the embodiment shown inFIG. 8B, the connecting structure 58 may pass around a lateral end 46 ofthe substrate 30. According to various embodiments, the connectingstructure 58 may be a bracket, a wire, a nanotube, a graphene sheet, ora graphene ribbon. The connecting structure 58 may be electricallyconductive. As described above, additional graphene sheets 10 orsubstrates 30 may be mounted on a free side of the first or secondgraphene sheets 10 a, 10 b in order to increase the number of layers inthe stack. Increasing the number of layers in the stack facilitates moreefficient use of three-dimensional space, thereby enabling smallersystems.

Referring to FIGS. 9A-9C, the flexible nature of graphene sheet 10 maybe used to facilitate construction of a circuit board 70. As shown, thegraphene sheet 10 includes a first portion 61, a second portion 62, anda third portion 63, and one or more devices 56 may be disposed on thegraphene sheet 10. The first portion 61 of the graphene sheet 10 may becoupled to a first side 36 a of a first substrate 30 a. The graphenesheet 10 is then folded or wrapped around the substrate 30 a, and thesecond portion 62 of the graphene sheet 10 may couple to the second side38 a of the substrate 30 a. A lateral end 66 of the substrate 30 may beconfigured to support the graphene sheet 10 as it transits from thefirst side 36 of the substrate 30 to the second side 38. As shown, thelateral end 66 may be configured to support a portion of the graphenesheet 10 between the first portion 61 and the second portion 62. Thelateral end 66 of the substrate 30 is contoured or rounded to reducestresses on the graphene sheet 10 and to prevent kinking or creasing ofthe sheet 10. A second substrate 30 b may be coupled to the free side ofthe second portion 62 of the graphene sheet 10, and the graphene sheet10 may be folded around the second substrate 30 b. The third portion 63of the graphene sheet 10 may then couple to the second side 38 b of thesecond substrate 30 b.

Referring to FIG. 9B, the second substrate 30 b may be disposed on thefree side of the first portion 61, and the graphene sheet 10 is thenfolded around the first and second substrates 30 a, 30 b. The thirdportion 63 of the graphene sheet 10 may then be disposed adjacent thesecond side 38 b of the second substrate 30 b.

According to one embodiment, the first and second substrates 30 a, 30 bof the embodiment of FIG. 9B are formed as one aerogel substrate 30. Forexample, a member 68 (e.g., flange, web, structure, element, etc.) maycouple the first substrate 30 a and the second substrate 30 b. Accordingto such an embodiment, the first portion 61 of the graphene sheet 10 maybe disposed between the first portion 30 a of the substrate 30 and thesecond portion 30 b of the substrate 30. The graphene sheet 10 may thenbe folded such that the second portion 62 of the graphene sheet 10 isdisposed adjacent to a second side 38 a of the first portion 30 a of thesubstrate 30, and then folded again such that the third portion 63 ofthe graphene sheet 10 is disposed adjacent a second side 38 b of thesecond portion 30 b of the substrate 30.

Constructing a circuit board 70 in these manners enables all of thedevices 56 of the circuit board 70 to be laid out on one graphene sheet70, which may be folded for compactness. This reduces or eliminates theneed for layer to layer connections (e.g., vias or edge connectors) asthe graphene sheet 10 continues from one layer to another. This mayreduce circuit board development time and complexity.

Referring to FIG. 9C, multiple graphene sheets 10 may be interwoven in astack of graphene sheets 10 and substrates 30. As shown, a firstgraphene sheet 10 a and a second graphene sheet 10 b are interwoven witha plurality of substrates 30. Interweaving the graphene sheets 10enables more efficient use of space and enables a minimum radius R to bemaintained in order to avoid kinking or creasing the graphene sheet 10.

Referring to FIG. 10, a flowchart of a process 100 for reducing phononiccoupling between a graphene monolayer and a substrate is shown,according to an exemplary embodiment. Process 100 is shown to includethe step of providing a substrate formed of aerogel (step 102). Process100 is further shown to include the step of disposing a monolayer filmof graphene on the substrate (step 104), for example, placing amonolayer film of graphene in contact with the substrate.

Referring to FIG. 11, a flowchart of a process 110 for reducing phononiccoupling between a graphene monolayer and a substrate is shown,according to an exemplary embodiment. Process 110 is shown to includethe steps of providing a substrate formed of aerogel (step 112),configuring a monolayer film of graphene and the aerogel substrate suchthat the graphene film and the aerogel substrate chemically bond (step114), disposing the graphene film on the substrate (step 116), andmechanically coupling the graphene film to the aerogel substrate (step118). According to various embodiments, the process 110 may only involvebonding the graphene to the substrate (step 114) or mechanicallycoupling the graphene to the substrate (step 118). In such embodiments,the step 118 or step 114, respectively, may be omitted.

Referring to FIG. 12, a flowchart of a process 120 for reducing phononiccoupling between a graphene monolayer and a substrate is shown,according to an exemplary embodiment. Process 120 is shown to includethe steps of providing a substrate formed of aerogel (step 122), heatinga monolayer film of graphene prior to disposing the graphene film on theaerogel substrate (step 124), and disposing the graphene film on thesubstrate (step 126).

Referring to FIG. 13, a flowchart of a process 130 for reducing phononiccoupling between a graphene monolayer and a substrate is shown,according to an exemplary embodiment. Process 130 is shown to includethe steps of providing a substrate formed of aerogel (step 132),disposing a monolayer film of graphene on the substrate (step 134),applying a first tensile force to the graphene film in a first direction(step 136), and tuning the force(s) applied to the graphene film (step140). Process 130 may further include the step of applying a secondtensile force to the graphene film in a second direction (step 138),which may also be tuned (step 140).

Referring to FIG. 14, a flowchart of a process 150 for reducing phononiccoupling between a graphene monolayer and a substrate is shown,according to an exemplary embodiment. Process 150 is shown to includethe steps of providing a substrate formed of aerogel (step 152),disposing a monolayer film of graphene on the substrate (step 154), anddisposing a second graphene film on the second side of the aerogelsubstrate (step 156). Process 150 may further include the step ofdisposing a second graphene film on the first graphene film opposite theaerogel substrate (step 158) or disposing a second aerogel substrate ona second side of the graphene film (step 160).

Referring to FIG. 15, a flowchart of a process 170 for reducing phononiccoupling between a graphene monolayer and a substrate is shown,according to an exemplary embodiment. Process 170 is shown to includethe steps of providing a substrate formed of aerogel (step 172), dopinga monolayer film of graphene (step 174), and disposing the graphene filmon the substrate (step 180). Process 170 may also include the steps ofdoping the graphene film with a non-carbon atom (step 176) and/or dopingthe graphene film with a functional group extending out of the grapheneplane (step 178).

Referring to FIG. 16, a flowchart of a process 200 for preservingelectronic properties in a mechanically supported graphene sheet isshown, according to an exemplary embodiment. Process 200 is shown toinclude the steps of providing a substrate formed of aerogel (step 202),providing a graphene film having one or more devices disposed thereon(step 204), and disposing the graphene film on the substrate (step 206).According to various embodiments, the device comprises a photoniccircuit, a plasmonic circuit, an electronic circuit, an integratedcircuit, a micro- or nano-electromechanical device.

Referring to FIG. 17, a flowchart of a process 210 for preservingelectronic properties in a mechanically supported graphene sheet isshown, according to an exemplary embodiment. Process 210 is shown toinclude the steps of providing a substrate formed of aerogel (step 212),doping a graphene film (step 214), disposing one or more devices on thegraphene film (step 216), and disposing the graphene film on thesubstrate (step 218). According to various embodiments, the doping maycomprises adding one or more defects to the graphene lattice, adding oneor more non-carbon atoms or molecules, or adding one or moreout-of-plane functional groups. It is also contemplated that thegraphene film may be doped (step 214) after the device is mounted on thegraphene film (step 216) or at substantially the same time, for example,the graphene film may be formed or grown to include the device and thedoping elements.

Referring to FIG. 18, a flowchart of a process 220 for preservingelectronic properties in a mechanically supported graphene sheet isshown, according to an exemplary embodiment. Process 220 is shown toinclude the steps of providing a substrate formed of aerogel (step 222),providing a first graphene film comprising one or more devices disposedthereon (step 224), disposing the first graphene film on the substrate(step 226), disposing a second graphene film on the substrate oppositethe first graphene film (step 228), and electrically coupling the firstgraphene film and the second graphene film (step 232). Process 220 mayalso include the step of disposing a third graphene film on the sameside of the substrate as the first graphene film (step 230). Accordingto various embodiments, the third graphene film may be disposed on thesubstrate (step 230) before the second graphene film is disposed on thesubstrate (step 228), after the first and second graphene films arecoupled (step 232), or at any time in between. According to otherembodiments, the third graphene film may be disposed on a lateral sideof the substrate, or on a side of the substrate opposite the firstgraphene film, for example, the same side as the second graphene film.

Referring to FIG. 19, a flowchart of a process 300 for forming a circuitboard is shown, according to an exemplary embodiment. Process 300 isshown to include the steps of providing a graphene film having one ormore devices disposed thereon (step 202), providing a substrate formedof aerogel, the substrate comprising a first side and a second sideopposite the first side (step 304), disposing a first portion of thegraphene film on the first side of the substrate (step 306), anddisposing a second portion of the graphene film on the second side ofthe substrate (step 308).

The construction and arrangement of the elements of the graphene-aerogelsystems and methods as shown in the exemplary embodiments areillustrative only. Although only a few embodiments have been describedin detail, those skilled in the art who review this disclosure willreadily appreciate that many modifications are possible (e.g.,variations in sizes, dimensions, structures, shapes and proportions ofthe various elements, values of parameters, mounting arrangements, useof materials, colors, orientations, etc.) without materially departingfrom the novel teachings and advantages of the subject matter recited.For example, elements shown as integrally formed may be constructed ofmultiple parts or elements. It should be noted that the elements andassemblies may be constructed from any of a wide variety of materialsthat provide sufficient strength or durability, in any of a wide varietyof colors, textures, and combinations. Additionally, in the subjectdescription, the word “exemplary” is used to mean serving as an example,instance or illustration. Any embodiment or design described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments or designs. Rather, use of the wordexemplary is intended to present concepts in a concrete manner.Accordingly, all such modifications are intended to be included withinthe scope of the present inventions. Other substitutions, modifications,changes, and omissions may be made in the design, operating conditions,and arrangement of the preferred and other exemplary embodiments withoutdeparting from the spirit of the appended claims.

The order or sequence of any process or method steps may be varied orre-sequenced according to alternative embodiments. Also two or moresteps may be performed concurrently or with partial concurrence. Anymeans-plus-function clause is intended to cover the structures describedherein as performing the recited function and not only structuralequivalents but also equivalent structures. Other substitutions,modifications, changes and omissions may be made in the design,operating configuration, and arrangement of the preferred and otherexemplary embodiments without departing from the spirit of the appendedclaims.

1-223. (canceled)
 224. An apparatus having reduced phononic couplingbetween layers comprising: an aerogel substrate; and a first monolayerof graphene coupled to the aerogel substrate.
 225. The apparatus ofclaim 224, further comprising a second layer of graphene supported bythe first monolayer of graphene opposite the aerogel substrate.
 226. Theapparatus of claim 225, wherein the second layer of graphene comprises amonolayer of graphene.
 227. The apparatus of claim 224, furthercomprising a second graphene layer; wherein the aerogel substratecomprises a first side and a second side, the first side configured tosupport the first monolayer of graphene, and the second side configuredto support the second layer of graphene.
 228. The apparatus of claim227, wherein the second graphene layer comprises a monolayer ofgraphene.
 229. The apparatus of claim 227, wherein the second side ofthe aerogel is disposed opposite the first side of the aerogel.
 230. Theapparatus of claim 227, further comprising a first electrical contactcoupled to the first monolayer of graphene and a second electricalcontact coupled to the second layer of graphene; wherein the firstmonolayer of graphene, the aerogel substrate, and the second layer ofgraphene are configured to form a capacitor.
 231. The apparatus of claim224, wherein the aerogel substrate comprises a first substantiallyhomogeneous surface disposed adjacent the first monolayer of graphene.232. The apparatus of claim 231, wherein the aerogel substrate comprisesa second substantially homogeneous surface disposed adjacent a secondmonolayer of graphene.
 233. The apparatus of claim 231, wherein theaerogel substrate comprises a second substantially structured surfacedisposed adjacent a second monolayer of graphene.
 234. The apparatus ofclaim 224, wherein the aerogel substrate comprises a first substantiallystructured surface disposed adjacent the first monolayer of graphene.235. The apparatus of claim 224, wherein the aerogel substrate comprisesa surface layer and a bulk layer, and wherein the properties of thesurface layer differ from the properties of the bulk layer.
 236. Theapparatus of claim 224, further comprising a second aerogel substrate;wherein the monolayer of graphene comprises a first side and a secondside disposed opposite the first side, the first side of the graphenesupported by the first aerogel substrate, and the second side of thegraphene supporting the second aerogel substrate.
 237. The apparatus ofclaim 224, wherein the monolayer of graphene comprises a macroscopicsheet.
 238. The apparatus of claim 224, wherein the monolayer ofgraphene comprises a non-carbon atom.
 239. The apparatus of claim 224,wherein the monolayer of graphene substantially defines a plane, andwherein the monolayer of graphene comprises a functional group extendingout of the plane.
 240. The apparatus of claim 224, wherein the monolayerof graphene is mechanically coupled to the aerogel substrate.
 241. Theapparatus of claim 240, wherein the mechanical coupling is configured toapply tension to the graphene sheet.
 242. The apparatus of claim 224,wherein the aerogel substrate is configured to apply a compressive forceto the graphene sheet.
 243. The apparatus of claim 224, wherein thefirst monolayer of graphene is in planar contact with a surface of theaerogel substrate.
 244. A system having preserved electronic propertiesin a supported graphene sheet comprising: a graphene sheet supported byan aerogel substrate; wherein the graphene sheet comprises one or moredevices.
 245. The system of claim 244, wherein the graphene sheetcomprises a monolayer.
 246. The system of claim 244, further comprisinga second graphene sheet supported by the first graphene sheet oppositethe aerogel substrate.
 247. The system of claim 244, further comprisinga second graphene sheet; wherein the aerogel substrate comprises a firstside and a second side, the first side configured to support the firstgraphene sheet, and the second side configured to support the secondgraphene sheet.
 248. The system of claim 247, wherein the first graphenesheet and the second graphene sheet are coupled by a connectingstructure.
 249. The system of claim 248, wherein the aerogel substratedefines a through-hole between the first graphene sheet and the secondgraphene sheet, the connecting structure passing therethrough.
 250. Thesystem of claim 248, wherein the connecting structure passes around alateral end of the aerogel substrate.
 251. The system of claim 244,further comprising at least one support structure.
 252. The system ofclaim 251, wherein the at least one support structure supports thegraphene sheet at a site where minimal perturbation of in-planeproperties is not important.
 253. The system of claim 251, wherein theat least one support structure is configured to apply tension to thegraphene sheet.
 254. The system of claim 244, wherein the aerogelsubstrate comprises a surface layer and a bulk layer, and wherein theproperties of the surface layer differ from the properties of the bulklayer.
 255. The system of claim 244, further comprising a second aerogelsubstrate; wherein the graphene sheet comprises a first side and asecond side opposite the first side, the first side of the graphenesheet supported by the first aerogel substrate, and the second side ofthe graphene sheet supporting the second aerogel substrate.
 256. Thesystem of claim 244, wherein the graphene sheet comprises a macroscopicsheet.
 257. The system of claim 244, wherein the graphene sheetsubstantially defines a plane, and wherein the graphene sheet comprisesa functional group extending out of plane.
 258. The system of claim 257,wherein the graphene sheet bonds to the aerogel substrate via one ormore functional groups.
 259. The system of claim 244, wherein thegraphene sheet is bonded to the aerogel substrate.
 260. The system ofclaim 244, wherein the graphene sheet is not bonded to the aerogelsubstrate.
 261. The system of claim 244, wherein the aerogel substrateis configured to apply a tensile force to the graphene sheet.
 262. Thesystem of claim 244, wherein the aerogel substrate is configured toapply a compressive force to the graphene sheet.
 263. A circuit board,comprising: a first substrate formed of aerogel, the first substratecomprising a first side and a second side opposite the first side; and agraphene film comprising a first portion and a second portion and havingone or more devices disposed thereon; wherein the first portion of thegraphene film is disposed adjacent the first side of the substrate, andwherein the second portion of the graphene film is disposed adjacent thesecond side of the substrate.
 264. The circuit board of claim 263,wherein the device comprises a photonic circuit.
 265. The circuit boardof claim 263, wherein the device comprises a plasmonic circuit.
 266. Thecircuit board of claim 263, wherein the device comprises an electroniccircuit.
 267. The circuit board of claim 263, wherein the devicecomprises an integrated circuit.
 268. The circuit board of claim 263,further comprising a second substrate formed of aerogel, the secondsubstrate comprising a first side and a second side opposite the firstside; wherein the first side of the second substrate is disposedadjacent the second portion of the graphene film opposite the firstsubstrate; and wherein a third portion of the graphene film is disposedadjacent the second side of the second substrate.
 269. The circuit boardof claim 263, further comprising: a second substrate formed of aerogel,the second substrate comprising a first side and a second side oppositethe first side; and wherein the first side of the second substrate isdisposed adjacent the first portion of the graphene film opposite thefirst substrate; and wherein a third portion of the graphene film isdisposed adjacent the second side of the second substrate.
 270. Thecircuit board of claim 263, wherein a lateral end of the first substrateis formed to support a portion of the graphene film between the firstportion and the second portion.